In the following question, the symbols +, −, *, /, and % are used with the…

Concept: Coded-inequality questions replace the standard relational signs (>, ≥, <, ≤, =) with arbitrary symbols. Solve them by: decoding every statement into its real inequality; chaining only variables that share a DIRECT relational link (two variables merely bounded from the same third variable, from opposite sides, are NOT thereby linked to each other); and treating a conclusion as definitely true only if every value assignment consistent with the statements satisfies it — a single valid counter-example is enough to break it. When two conclusions are not a complementary pair over the same two variables, there is no guarantee that at least one of them must hold.

Application:

Decoding the key: + is >, − is ≥, * is <, / is ≤, % is =.

1. Decode the statement: S+T → S > T; U*S → U < S; T*S → T < S (restates S > T); S−M → S ≥ M; Q−R → Q ≥ R (about Q and R only, irrelevant to the conclusions).

2. Conclusion 1 (T+U) claims T > U. T and U are each compared only to S (S > T and U < S), from opposite sides — no direct link between T and U. S = 3, T = 2, U = 2.5 satisfies every statement and gives T < U; S = 3, T = 2, U = 1 also satisfies every statement and gives T > U. Since both are possible, T > U is not guaranteed.

3. Conclusion 2 (M/T) claims M ≤ T. M and T are each compared only to S (S ≥ M and S > T), again from opposite sides — no direct link between M and T. S = 4, M = 3, T = 2 satisfies every statement and gives M > T; S = 4, M = 1, T = 2 also satisfies every statement and gives M ≤ T. Since both are possible, M ≤ T is not guaranteed either.

4. Checking 'either conclusion 1 or 2': the two conclusions concern different variable pairs (T,U) and (M,T), not a complementary split of one pair, so there is no structural reason at least one must hold.

Cross-check: A single assignment can defeat both conclusions together: S = 10, T = 2, U = 3, M = 8 satisfies every statement (S > T, U < S, T < S, S ≥ M), yet T > U is false (2 is not greater than 3) and M ≤ T is false (8 is not ≤ 2) — both fail at once. Since neither conclusion holds in every case, and no case forces at least one to hold, the correct choice is that neither conclusion 1 nor conclusion 2 is true.